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Mathematics > Combinatorics

Title:Accessibility in transitive graphs

Abstract: Confirming a conjecture of Diestel, we prove that every locally finite
transitive graph whose cycle space is generated by cycles of bounded length is
accessible. This also implies Dunwoody's conjecture that locally finite
hyperbolic transitive graphs are accessible. As a further application, we
obtain a combinatorial proof of Dunwoody's accessibility theorem of finitely
presented groups.